Weight painting mode right click action differs from time to time
If the armature is in pose mode, and you select the skinned object, it will let you pose the armature if you select any bone. On the other hand, if the armature is in object mode it will take you back to object mode. 

Actually, this is standard for all objects in that selection by right-clicking in the viewport will put the viewport in whatever mode that object was last in. 



Note that selecting another object in edit mode or particle edit mode will not work.